A causal proportional hazards estimator under homogeneous or heterogeneous selection in an IV setting

  • Ditte Nørbo Sørensen
  • Torben MartinussenEmail author
  • Eric Tchetgen Tchetgen


In this paper we present a framework to do estimation in a structural Cox model when there may be unobserved confounding. The model is phrased in terms of a selection bias function and a baseline model that describes how covariates affect the survival time in a scenario without exposure. In this way model congeniality is ensured. The method uses an instrumental variable. Interestingly, the formulated model turns out to have similarities to the so-called Cox–Aalen survival model for the observed data. We exploit this to enhance estimation of the unknown parameters. This also allows us to derive large sample properties of the proposed estimator.


Causal effect Structural Cox model Instrumental variable Treatment effect on the treated Selection bias function 



We are grateful to Shoaib Afzal and Børge Nordestgaard for giving us access to the CGPS-data.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Section of BiostatisticsUniversity of CopenhagenCopenhagen KDenmark
  2. 2.Statistics DepartmentWharton, University of PennsylvaniaPhiladelphiaUSA

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